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The  Weight  of  a  Falling  Drop  and  the  Laws  of 
Tate.      The  Determination  of  the  Molec- 
ular Weights  and    Critical   Temper- 
atures of  Liquids  by  the  Aid 
of  Drop  Weights. 


BY 


RESTON  STEVENSON,  A.B.,  A.M. 


DISSERTATION 


SUBMITTED  IN   PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 
THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE  FACULTY  OF 
PURE  SCIENCE  IN  COLUMBIA  UNIVERSITY,  IN  THE 
CITY  OF  NEW  YORK. 


NEW  YORK  CITY. 
1908 


EASTON,  PA.  : 
ESCHENBACH  PRINTING  Co. 

1908. 


The  Weight  of  a  Falling  Drop  and  the  Laws  of 
Tate.      The  Determination  of  the  Molec- 
ular Weights  and    Critical   Temper- 
atures of  Liquids  by  the  Aid 
of  Drop  Weights. 


BY 


RESTON  STEVENSON,  A.B.,  A.M. 


DISSERTATION 


SUBMITTED  IN   PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR 
THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  THE  FACULTY  OF 
PURE  SCIENCE  IN  COLUMBIA  UNIVERSITY,  IN  THE 
CITY  OF  NEW  YORK. 


NEW  YORK  CITY. 
1908 


E ASTON,  PA.: 

ESCHENBACH  PRINTING  Co. 
1908. 


at 

•>A-^      / 


CONTENTS. 


I.  Introduction.  Object  of  investigation 5 

II.  Apparatus  and  method 9 

III.  Results H 

IV.  Discussion  of  results l8 

V.     Summary 22 


183469. 


ACKNOWLEDGMENT. 


This  piece  of  work  was  suggested  by  Professor  J.  L.  R.  Morgan  and 
was  carried  out  under  his  direction.  Mr.  Higgins  has  helped  the  author 
in  his  preparation  of  this  paper  for  publication. 

R.  S. 


OF  THE 

UNIVERSITY 

OF 


The  Weight   of   a   Falling  Drop   and  the  Laws   of 

Tate.      The   Determination   of   the   Molecular 

Weights    and    Critical    Temperatures    of 

Liquids  by  the  Aid  of  Drop  Weights* 


Introduction.    Object  of  the  Investigation. 

In  1864,  Thomas  Tate,1  as  the  result  of  his  experiments  with  water, 
announced  the  following  laws: 

I  Other  things  being  the  same,  the  weight  of  a  drop  of  liquid  (falling 
from  a  tube)  is  proportional  to  the  diameter  of  the  tube  in  which  it  is 
formed. 

II.  The  weight  of  the  drop  is  in  proportion  to  the  weight  which  would 
be  raised  in  that  tube  by  capillary  action. 

III.  The  weight  of  a  drop  of  liquid,  other  things  being  the  same,  is 
diminished  by  an  augmentation  of  temperature. 

Tate's  experiments  were  all  made  with  thin- walled  glass  tubing  vary- 
ing in  diameter  from  o.  i  to  0.7  of  an  inch,  the  orifice  in  each  case  being 
ground  to  a  "sharp  edge,  so  that  the  tube  at  the  part  in  contact  with  the 
liquid  might  be  regarded  as  indefinitely  thin."  His  weights  were  cal- 
culated from  the  weight  of  from  five  to  ten  drops  of  liquid,  which  formed 
at  intervals  of  40  seconds,  and  were  collected  in  a  weighed  beaker. 

Tate's  law  as  we  know  it  to-day,  is  supposed  to  be  a  summation  of 
the  first  two  laws  of  Tate,  but  it  must  be  said  that  it  attributes  to  Tate 
a  meaning  that  he  never  indicated  and  probably  never  intended.  The 
analytical  expression  of  this  faulty  law  is  the  familiar 

W  =  2Trry, 

where  Wis  the  weight  of  the  falling  drop,  r  the  radius  of  the  tube  on 
which  it  forms,   and  y  is  the  surface  tension  of  the  liquid.      Of  course, 

1  Phil.  Mag.,  4th  Ser.,  27,  176  (1864).     All  other  references  to  drop  weight  will 
be  found  in  the  bibliography  of  that  subject  at  the  end  of  this  paper. 


Tate's  second  law  shows  drop  weight  to  be  proportional to  surface  tension, 
for  the  weight  of  a  liquid  rising  in  a  tube  by  capillary  action  is  propor- 
tional to  surface  tension;  and  his  first  law  shows  drop  weight  to  be  pro- 
portional  to  the  diameter  (or  radius)  of  the  tube;  but  he  did  not  even 
imply  that  drop  weight  is  equal  to  the  product  of  the  circumference  of 
contact  into  the  surface  tension.  The  real  anyltical  expression  of  Tate's 
first  two  laws  as  he  actually  announced  them,  in  place  of  the  obove, 
shold  be 

W=KjD, 

where  K^  is  a  constant,  and  D  is  the  diameter  of  the  tube;  or,  when  the 
drops  are  all  formed  on  the  same  tube  (z.  <?.,  where  D  is  constant), 

W=Ki, 
K  being  a  new  constant. 

Guye  and  Perrot,  Ollivier,  Lohnstein  and  others  in  their  bibliograph- 
ical summaries  have  similarly  misunderstood  Tate's  laws. 

Lebaigue  showed  experimentally  that  when  2  r  applies  to  the  cir- 
cumference of  the  bore  of  the  capillary  tube  that  the  equation  which 
has  been  assigned  to  Tate  is  not  even  remotely  true,  but  that  the  weights 
of  the  drops  are  nearly  proportional  to  the  circumference  of  the  lower 
surface  of  the  tube.  In  Tate's  work,  as  stated,  the  external  and  internal 
diameters  of  the  tube  at  the  outlet  were  practically  the  same.  Hagen 
has  shown  that  in  the  above  equation  r  the  radius  of  the  tube  does  not 
equal  the  radius  of  the  drop  at  its  point  of  separation  because  of  the 
meniscus  which  remains  behind,  kayleigh  proposed  the  equation 
W  =  3,8r,  but'this  did  not  give  accurate  results  except  with  a  very  few 
liquids.  Duclaux  proposed  the  equation  W  =  Kr,  and  by  this  formula 
he  determined  surface  tension  with  his  "count  pipette;"  counting  the 
number  of  drops  which  a  certain  weight  of  liquid  would  give.  He  found 
that  K  varied.  Lohnstein  used  this  same  equation  except  that  he  de- 
rived mathematically  in  a  purely  theoretical  paper  a  table  with  which 
he  attempted  to  determine  K  for  each  value  of  r.  He  made  K  a  geometri- 
cal function  of  r.  All  of  these  corrections,  however,  were  corrections 
for  the  variations  of  drop  weight  with  the  size  of  the  outlet  of  the  tube. 
The  variations  for  different  liquids  still  remained  uncorrected  and  unac- 
counted for. 

Duclaux,  Buhrer,  Yvon,  Ollivier,  and  others  have  shown  how  the 
weight  of  the  drop  varied  with  the  temperature,  the  nature  of  its  atmos- 
phere, electrical  conditions,  mechanical  jarring,  speed  of  outflow,  etc., 


yet  when  the  conditions  were  made  constant  and  all  disturbing  factors 
removed,  the  determination  of  surface  tension  by  the  method  of  drop 
weights  still  remained  inaccurate. 

Drops  of  different  sizes,  from  different  kinds  and  forms  of  surfaces, 
drops  made  with  different  speeds  of  outflow,  (Gugliemo,  Frankenheim, 
Hagen,  Guthrie,  Ouincke,  Lenard,  Forch,  Guye  and  Perrot,  Rosset,) 
have  been  studied  and  interesting  data  obtained.  Drops  have  been  photo- 
graphed (Lenard)  and  projected  (Worthington) ,  their  forms  calculated 
mathematically  (Mathieu,  Dupre,  Bertrand,  Duclaux)  and  the  vibra- 
tion of  drops  when  about  to  fall  studied  (Rayleigh).  Other  data  have 
been  obtained  (Quincke)  but  no  method  has  been  obtained  by  which 
surface  tension  can  be  accurately  determined  from  falling  drops. 

The  cause  of  the  inaccuracy  of  the  drop  weight  methods  for  surface 
tension  has  been  ascribed  by  Antonow  and  others  to  the  unequal  wetting 
of  the  surfaces  of  the  outlet  by  the  different  liquids.  Also  no  known 
property  of  liquids  has  been  found  according  to  which  the  errors  in  the 
surface  tension  determinations  varied  (Hanney).  Such  a  variation 
did  not  occur  regularly  with  the  variation  in  the  density,  chemical  com- 
position, viscosity,  refractive  index,  etc.  Therefore,  these  variations 
have  been  ascribed  to  a  property  of  the  liquids  which  is  as  yet  unknown, 
and  therefore  the  errors  were  considered  unavoidable  and  impossible 
of  correction  (Guye). 

Two  methods  have  been  tried  to  prevent  this  unequal  wetting  by 
different  liquids  of  the  surface  of  the  outlet: 

(i)  The  sides  of  the  tube  or  the  surface  of  the  exit  nearly  to  the  bore 
were  covered  with  a  layer  of  some  grease,  of  arsenic  trioxide  or  of  lycop- 
odiurn  powder,  etc.,  (Ollivier).  It  was  found  that  in  this  way  accurate 
results  could  sometimes  be  obtained.  However,  the  layer  was  dissolved 
by  the  liquids  used,  thus  lowering  greatly  and  to  a  varying  extent  the 
surface  tension  of  the  liquids  used,  and  the  layer  would  sometimes  be 
unevenly  wetted  at  the  small  points  and  would  wash  away  unevenly. 
Therefore,  while  a  perfect  layer  of  grease  would  give  an  outlet  with  which 
accurate  results  could  be  obtained,  in  actual  experiment  the  results  were 
found  to  be  unreliable  (Lebaigue,  Traube).  Ollivier  has  discussed  the 
defects  of  these  layers  and  has  recommended  for  the  outlet  of  the  tube 
a  metal  disc  with  a  small  hole,  the  disc  to  be  slightly  greased  with 
paraffin  up  to  the  hole  and  then  this  layer  to  be  thoroughly  and  thinly 


8 

coated  with  soot.  He  gives  only  one  experimental  determination  to 
support  his  claim  that  accurate  results  are  obtained  by  this  method 
and  this  one  result,  with  water,  is  not  accurate. 

(2)  The  second  method  for  the  preventing  of  unequal  wetting  of  the 
surfaces  by  different  liquids  is  that  the  one  proposed  by  Antonow.  The 
outlet  tube  is  immersed  in  a  (comparatively)  non-miscible  liquid.  The 
liquid  bath  prevents  the  liquid  in  the  tube  from  wetting  at  all  the  bot- 
tom surface  of  the  tube,  so  that  all  the  drops  fall  from  the  bore  of  the 
tube.  However,  apart  from  the  experimental  difficulties  this  method 
does  not  measure  the  surface  tension  of  the  pure  liquid  A  but  of  a  satur- 
ated solution  of  liquid  B  in  liquid  A.  This,  of  course,  varies  with  differ- 
ent pairs  of  liquids  used  and  with  the  temperature. 

The  general  result  of  the  work  of  all  other  investigators  since  the  time 
of  Tate,  on  the  subject  of  drop  weight,  may  be  summed  up  best,  perhaps, 
in  the  words  of  Guye  and  Perrot  (1903),  vis.: 

"The  law  of  the  proportionality  of  the  weight  of  a  drop  to  the  diameter 
of  the  tube  is  no  more  generally  justified  than  that  of  the  proportionality 
of  the  weight  to  the  surface  tension." 

"  The  laws  of  Tate  are  not  general  laws,  and,  even  in  the  case  of  static 
(slow  forming)  drops,  represent  only  a  first  approximation." 

It  will  be  seen  from  these  conclusions  that  Guye  and  Perrot  repudiate 
not  only  the  form  of  Tate's  law  as  we  know  it  to-day,  but  also  his  first 
two  laws  in  the  form  that  he  announced  them.  It  must  be  said,  however, 
that  no  investigator  has  as  yet  fairly  tested  Tate's  laws,  for  no  one  has  as  yet 
exactly  reproduced  Tate's  conditions.  Practically  all  the  results  thus 
far  obtained  have  been  for  drops  forming  on  capillary,  instead  of  on  thin- 
walled  tubes;  and  the  effect  produced  by  the  "sharp  edge"  of  the  drop- 
ping tube,  as  described  by  Tate,  has  never  been  even  approximately  ap- 
proached, except  under  such  conditions  that  the  results  were  obscured 
by  other  factors  (Ollivier,  Antonow). 

The  object  of  this  investigation,  is  to  test  the  truth  of  Tate's  law  (and 
especially  the  second),  as  he  originally  stated  them,  more  fairly  and  with 
greater  accuracy  than  has  hitherto  been  done,  reproducing  his  conditions  in 
a  way  that  others  have  failed  to  do,  paying  particular  attention  to  the  effect 
of  the  form  of  the  tip,  and  excluding  those  errors  which  are  so  apparent  in  the 
work  of  some  of  the  previous  investigators.  And  it  was  hoped  that  even  if 


9 

Tate's  laws  were  found  not  to  hold  rigidly,  it  might  still  be  possible  to  em- 
ploy the  temperature  coefficient  of  drop  weight  of  any  one  liqiud,  in  a 
formula  similar  to  that  of  Ramsay  and  Shields,1  in  place  of  their  tempera- 
ture coefficient  of  surface  tension,  as  a  means  of  ascertaining  molecular 
weight  in  the  liquid  state,  and  the  critical  temperature. 

It  may  be  said  here,  to  anticipate,  that  the  results  of  this  work  have 
proven  to  be  even  better  than  was  hoped,  for  they  have  shown  that 
not  only  molecular  weights  in  the  liquid  state  and  critical  tempera- 
tures, can  be  calculated  just  as  readily  and  accurately  from  the 
temperature  coefficient  of  drop  weight,  as  from  that  of  surface  tension; 
but  also  that  the  relative  surface  tensions  of  various  liquids  can  be  found 
from  drop  weights,  and  that,  thus  found,  they  agree  with  those 
determined  by  the  capillary  rise  as  well  as  do  those  by  any  of  the 
other  methods,  and  almost  as  well  as  those  for  the  same  liquid  by  the 
same  method,  carried  out  by  different  observers.  This  relation  to  sur- 
face tension  is  true  for  the  interpolated  values  of  surface  tension,  and 
further  work,  using  the  actual,  experimental  values,  will  probably  only 
show  the  relation  to  be  even  more  rigid  than  this. 

Apparatus  and  Method. 

In  order  to  avoid  the  complication  which  might  be  introduced  by  the 
successive  formation  of  several  drops,  I  have  measured,  throughout 
this  work,  the  volume  of  a  single  drop,  for  that  method,  under  these  condi- 
tions, is  far  more  accurate  and  delicate  than  any  weighing  method. 

Although,  unlike  Tate,  I  have  used  capillary  tips  upon  which  the 
drop  forms,  they  were  so  constructed  them  that  one  might  expect  to  ob- 
tain an  effect  similar  to  that  obtained  by  Tate  with  the  "sharp  edge" 
of  his  thin- walled  tube.  Apparently  the  effect  of  this  "sharp  edge" 
is  to  delimit  the  area  of  the  tube  upon  which  the  drop  can  hang,  and  to 
prevent  the  liquid  rising  upon  the  outer  walls  of  the  tube.  The  form  of 
tip  employed  in  the  measurements  is  shown,  in  section,  in  Fig.  i(O'), 
both  the  bottom  and  bevel  being  highly  polished. 

Observation  of  a  tip  of  this  form  shows  that  it  behaves  exactly  as  such 
a  one  as  described  by  Tate,  and  that  the  lower  edge  of  the  bevel,  just  as 
Tate's  "sharp  edge,"  is  the  limit  of  the  area  upon  which  the  drop  hangs, 
provided,  of  course,  that  its  diameter  is  less  than  that  of  the  maximum 
drop  of  the  liquid  with  the  smallest  maximum  drop.  The  liquid  forming 
-a  drop  on  this  tip  does  not,  under  any  condition,  rise  to  wet  the  bevel  or 
1  Zeit,  f.  phys.  Chem.,  12,  431  (1893). 


10 


walls  of  the  tithe  as  it  might  on  an  ordinary  one.  This  effect  has  also  been 
obtained,  during  the  course  of  our  work,  by  two  other  investigators 
(Antonow  and  Ollivier), 
but  only  by  the  use  of 
foreign  substances,  which 
contaminate  the  liquid. 

The  complete  appara- 
tus used  in  the  prelimi- 
nary experiments  is 
shown  in  section,  in  Fig. 
i .  P  is  a  translucent  por- 
celain scale,  55  centime- 
ters long,  divided  into 
millimeters.  AB  is  a 
capillary  burette  of  such 
a  bore  that  i  millimeter 
contains  about  0.0003  cc. 
This  tube  was  carefully 
calibrated  with  mercury, 
and  a  curve  prepared, 
from  which  the  volume 
between  any  two  scale 
readings  could  be  found. 
One  end  of  this  burette, 
A,  was  connected  by  rub- 
ber tubing  to  the  rubber 
compression  bulb  K.  This 
bulb  was  so  arranged  in 
a  screw  clamp  that  the 
pressure  upon  it  could  be  gradually  increased  or  decreased,  thus  giving  abso- 
lute and  delicate  control  over  the  movement  of  the  liquid  in  the  burette.  The 
larger  tubing  BC,  which  is  the  continuation  of  the  tip,  passes  through  the 
rubber  stopper  R,  and  thus  supports  the  dropping  cup  D.  F  is  a  dipper 
which  can  be  raised,  lowered,  or  swung  around  to  any  position  by  means  of 
the  rod  G.  From  this  the  burette  can  be  filled  with  liquid,  and  into  it  the 
drop  from  the  tip  O  ultimately  falls.  The  bottom  of  the  cup  D  is  covered 
with  a  thin  layer  of  the  liquid,  and  the  tube  H,  through  which  G  passes,  is 
stuffed  with  filter  paper,  saturated  with  the  liquid. 


Fig.   I. 


II 

The  object  of  this  form  of  apparatus  was  to  prevent  evaporation  of  the 
liquid  of  the  drop,  and  to  enable  one  to  measure  drop  volumes  at  any  de- 
sired temperature,  by  immersing  the  entire  apparatus  to  the  point  m  in 
a  waterbath. 

Before  making  a  measurement  with  this  apparatus,  the  cup,  dipper, 
tube  and  tip  are  thoroughly  cleansed  with  chromic-sulphuric  acid,  water, 
alcohol,  and  ether,  and  dried  by  a  current  of  air.  The  liquid  is  then  placed 
in  the  cup  and  in  the  dipper,  from  which,  after  the  stopper  R  is  fastened 
tightly,  the  tube  is  filled  to  such  an  extent  that  the  lower  meniscus  is  just 
about  to  enter  the  tip  O  when  the  other  end  of  the  column  (in  the  burette 
tube  A B)  is  at  zero,  or  some  point  just  below  it.  This  point  (the  zero  point) 
is  then  recorded,  and  the  bulb  very  gradually  compressed  until  the  drop 
formed  at  the  tip  O  falls  off.  The  reading  of  the  other  end  of  the  column, 
at  the  instant  of  fall,  then  enables  one,  knowing  the  zero-point,  to  find  the 
volume  of  the  maximum  drop  that  can  form  on  the  tip ;  I  shall  designate 
this  as  the  pendant  drop  (P.  D.).  By  drawing  the  liquid,  that  is  left  on  the 
tip,  back  into  the  tube  again,  until  the  lower  meniscus  is  once  more  just 
about  to  enter  the  tip  0,  it  is  possible  to  find  the  volume  of  the  drop  that 
has  remained  clinging  to  O\  this  I  shall  call  the  clinging  drop  (C.  D.). 
Subtracting  the  volume  of  this  from  that  of  the  pendant  drop,  one  finally 
finds  the  volume  of  the  falling  drop  (F.  D.). 

Experiments  with  this  preliminary  apparatus  showed  the  method  to  be 
excellent,  but  made  apparent  the  fact  that  greater  delicacy  was  desirable. 
The  second,  and  final  form  of  apparatus,  as  shown,  in  section,  in  Fig.  2, 
is  simply  a  modification  of  the  first.  Here  the  dropping  tube  is  sealed 
into  a  glass  stopper,  and  the  cup  is  provided  with  a  wide  rim  to  allow  the 
use  of  mercury  as  a  seal.  An  elastic  band,  passed  from  the  hooks  Q  over 
the  stopper,  and  between  the  two  tubes,  holds  stopper  and  cup  together, 
rnd  prevents  the  passage  of  either  mercury  or  the  water  of  the  bath  into 
the  cup.  To  obtain  a  more  delicate  setting,  in  determining  the  zero-point, 
than  is  possible  by  observing  the  passage  of  the  meniscus  into  the  tip, 
the  dropping  tube,  here,  is  constricted  at  5,  and  the  lower  meniscus,  in  all 
readings,  is  held  to  a  mark  at  that  point. 

Two  pieces  of  apparatus  in  this  form  were  used,  the  burette  in  one  case 
(tube  2)  holding  approximately  0.000,08  cc.,  and  the  other  (tube)  30.000,056 
cc.  per  millimeter.1  In  order  that  a  scale  of  the  same  length  as  before 
might  be  used,  these  measuring  tubes  were  bent  in  the  form  shown  in  Fig. 

1  These  tubes  were  calibrated  with  mercury  at  room  temperature,  and  no  cor- 
rection in  volume  was  made  when  they  were  used  at  higher  temperatures,  for  the  varia- 
tions were  found  to  be  well  within  the  experimental  error. 


12 


2.  In  tube  2  there  were  three  small 
bulbs  blown  in  the  first  length  of 
the  burette,  while  tube  3  had  a  single 
bulb  V,  with  an  approximate  capac- 
ity of  0.027  cc.  The  use  of  a  bulb 
or  bulbs  enabled  one  to  get  the  total 
volume  of  liquid  necessary  for  a 
drop,  without  an  excessive  length  of 
the  tubing.  For  liquids  forming 
drops  of  large  volume,  the  zero- 
point  must  be  above  the  bulb  or 
bulbs;  for  those  giving  smaller  vol- 
umes it  must  be  below  the  single 
bulb,  or,  in  case  there  are  three 
bulbs,  below  one  or  more  of  them.  l|| 

With  these  pieces  of  apparatus, 
only  the  volumes  of  the  falling  drops 
were  measured,  for  the  results  with  the 
first  apparatus  showed  that,  of  the 
three  kinds  of  drops,  they  only  were 
related  to  surface  tension.  The  rea- 
son for  originally  determining  the 
volumes  of  all  three  kinds  of  drops, 
when  Tate  considered  only  the  fall- 
ing drop,  was  the  suggestion  of 
Ostwald1  that  the  pendant  drop  from 
a  capillary  tube  would  probably  cor- 
respond to  falling  drop  from  a  thin- 
walled  tube,  such  as  Tate  used.  Ex- 
periment shows,  however,  that  here, 
also,  the  falling  drop  is  the  impor- 
tant factor. 

To  measure  the  volume  of  the  fall- 
ing drop  with  this  piece  of  appara- 
tus, the  zero-point  is  found,  just  as 
before,  by  drawing  the  liquid  back 
into  the  burette,  until,  when  the 


V 


Fig.  2. 


1  Hand-  und  Hilfsbuch  zur  ausftihrung  Physiko-chemischer  Messungen. 
1893,  PP-  300-301. 


upper  meniscus  is  at  zero  or  just  below  it,  the  lower  meniscus  is 
exactly  at  the  mark  in  the  constricted  portion  of  the  tube  5;  then, 
as  before,  the  liqiuid  is  very  gradually  forced  over  until  the  drop  on 
the  tip  O  falls  off.  No  reading  for  the  pendant  drop  is  attempted, 
but  the  liquid  is  at  once  drawn  back  to  the  mark,  and,  after  allowing  suffi- 
cient time  for  drainage,  the  position  of  the  upper  meniscus  is  observed. 
The  difference  in  volume  of  the  burette  tube,  between  the  zero-point  and 
the  latter  point,  is  then  the  volume  of  the  drop  that  has  fallen.  The  pres- 
sure on  the  rubber  bulb  in  all  cases  must  be  increased  very  gradually  at 
the  instant  when  the  drop  is  about  to  fall,  for  a  sudden  increase  in  pressure 
at  that  time  tends  to  increase  the  volume  of  the  falling  drop. 

It  was  necessary  before  using  these  delicate  forms  of  apparatus  to  prove 
conclusively  that  no  evaporation  takes  place  from  the  drop  as  it  is  forming. 
To  ascertain  this  the  tube  was  filled  with  liquid,  and  the  zero-point  noted. 
Then  gradually  the  pressure  on  the  bulb  was  increased  until  a  large  drop, 
though  not  sufficiently  large  to  fall,  was  formed  at  O.  After  standing  in 
this  condition  for  several  minutes,  care  being  taken,  as  it  must  always  ber 
that  the  apparatus  was  not  jarred  or  disturbed,  the  liquid  is  drawn  back 
until  the  lower  meniscus  is  again  at  the  mark  at  5.  Any  decrease  in  vol- 
ume of  the  liquid,  from  that  originally  observed,  is  then  to  be  attributed, 
with  such  tips  as  were  used,  to  evaporation  from  the  drop.  Even  the 
first  observations  for  this  purpose,  however,  showed  that  there  was  no 
evaporation,  for  one  invariably  found  an  increase  in  the  volume  of  the  liquid, 
instead  of  a  decrease;  in  other  words,  liquid  was  always  deposited  upon  the 
hanging  drop,  no  matter  how  often  it  was  formed  and  drawn  back.  After 
a  number  of  attempts  to  avoid  this  deposition  upon  the  forming  drop, 
by  partially  filling  the  cup  with  glass  beads,  sand,  or  filter  paper,  moistened 
with  the  liquid ,  and  also  by  the  use  of  a  vertically  placed  bundle  of  short 
closed  tubes,  each  filled  with  the  liquid  and  presenting  a  meniscus  of  ap- 
proximately the  diameter  of  the  drop  itself,  it  was  found  that  it  could  be 
avoided  entirely  by  depositing  the  liquid  (before  the  experiment)  as  a  fog,  upon 
the  walls  of  the  cup  D.  This  fog  can  be  produced  very  readily  by  heating 
the  cup  in  a  waterbath  (after  the  apparatus  has  been  set  up  and  filled) 
10°  to  20°.  In  this  way  minute  drops  of  the  liquid  are  deposited  upon 
the  walls  of  the  cup,  and  change  the  condition  within,  so  that  there  is  then 
neither  evaporation  from  the  hanging  drop,  nor  deposition  upon  it,  and  the 
upper  meniscus  always  returns  to  the  same  point,  no  matter  how  often 
the  drop  may  be  formed  and  drawn  back.  Before  each  measurement 
it  was  made  certain,  in  this  way,  that  such  a  condition  was  attained. 

It  will  be  seen  that  the  delicacy  of  this  method  depends  simply  upon  the 
size  of  the  capillary  tubing  used  as  the  burette.  Tube  3(1  mm.  =  0.000,056 
cc.)  was  the  smallest  tubing  available  at  the  time,  except,  of  course,  the 


very  narrow  thermometer  tubing,  which  offered  too  great  a  resistance  to 
the  flow  of  liquids,  for  this  purpose.1 

In  all  cases  the  apparatus  was  immersed  in  a  waterbath  with  transparent 
sides,  the  temperature  of  which  was  kept  constant  to  the  point  within  o .  i  °. 

Results. 

In  Tables  I,  II,  and  III  are  given  the  results  for  drop  volumes  and  drop 
weights,  and  the  relation  observed  between  drop  weight  and  surface  ten- 

TABLE  I. 

Diameter  of  tip  =  0.622  cm.  approximately,     i  mm.  on  burtte  =  0.0003  cc. 

Weight  of  drop  _  w 
Surface  tension  *"  7 


Substance. 

Ether 

dyi 
Temp. 
2O  O 

Surface 
tension, 
ics  per  cm, 

16.80 
29.38 
30.00 
32.  io 

37.35 
39.19 
44.10 

45.13 

70.60 

Weights  of  drop  in  mgs. 

WP.D. 
34-6 
56.0 
53-2 
66.0 
78.5 
77-3 
81.8 
86.6 

127.  I 

WF.D. 
21.4 
35-2 
36.1 
41.4 
5O.O 
49.8 
52.9 
57.o 
80.  i 

Wc.D. 

13.2 

20.  6 

17.2 
24.6 
28.4 
27.6 
28.7 
29.6 
37  .  .S 

Benzene  

.     22.  5 

Ethyl  iodide 

10    I 

Chlorbenzene.  .  .  . 
Guaiacole2 

.     2O.  O 

io  6 

Benzaldehyde.  .  . 
Aniline 

..  15.4 

.     17    5 

Quinoline 

je    A 

Water.  . 

.     20.0 

KP.D.      KF.D. 

KC.D. 

2.06 

.27 

0.79 

1.91 

.21 

0.71 

1.77 

.20 

0.57 

2.05 

•30 

0.77 

2.10        [ 

•34] 

0.76 

1.97 

.27 

0.71 

1.86 

.  21 

0.65 

1.92 

.26 

0.65 

i.  80 

.26 

0.53 

Diameter  of  tip 


Substance. 
Benzene. . 


Temp. 
30-5 

"         60.7 

Chlorbenzene ...   28.5 
...  65.0 

Aniline 27.8 

"      58.2 

Quinoline 28.0 

"        65.0 

Water 25.5 

"     56-9 

"     79-2 


Kp.D.= 


Average  KF.D.  =  i.248±o.oi2 
Mean  error  of  a  single  result  =  ±0.035 
TABLE  II. 
0.62  cm.  approximately,     i  mm.  on  burette  =  0.00,008  cc. 

Weight  of 

falling  drop 

in  mgs. 

WF.D. 

33.64 
28.50 
39.10 
34-07 
50.99 
45.91 
53.58 
48.47 
87-85 
80.55 
75.20 


Volume  of 

falling  drop, 

cc. 

0.03880 
0.03420 
0.03561 
O.O3220 
0.05033 
0.04675 
0.04912 
0.04572 
0.08812 
0.08180 
0.07742 


Specific 
gravity. 

0.867 

0.833 

1.098 

1.058 

I.OI3 

0.982 

1.091 

1. 060 

0.9969 

0.9848 

0.9722 


Surface  ten- 
sion, dynes 
per  cm. 

7 

26.58 
22.77 
31.02 
26.91 
40.69 
37.32 
42.30 
38.22 
69.70 
64.79 
60.97 


Average  KF.D.  =  i . 253  ±  o  004 


Mean  error  of  a  single  result  =  ±0.013 
1  It  has  since  been  possible  to  obtain  still  smaller  tubing,  and  the  work  is  now 

being  continued  in  this  laboratory  with  a  burette  on  which  i  millimeter  corresponds 

to  about  0.000,046  cc. 

*  Commercial  and  impure;  omitted  in  computing  the  average. 


15 


t 


ft 


ff 


Substance. 


NO-*".    «  Oi    w  01  Oi  Oi  Oi    M    Temp. 

*4    ON«>»     O^JOiOi^l     10     00 


g 


a-S 


oooooooooo 


O  O  O  0 
4*.  4*  4*  4* 
K>  00  4»  0 


Oi  Oi  Oi  Oi    Volumeoffallingdrop.ee. 


vO     «    ^4   vO    4»-    Oi    Oi     M    On    4* 
•*jOwtotOf*tovoONOi 

M«OMOOMMOO 

bbobioOMOooo  Specific  gravity. 

4*vo-4Mtost-£>O>o^i 
vO  4*  O  00  vO 


ON  vO  4>.  O  Oi 


OO  00  00  Cn 
n  Oi  00  Ol 


Weight  of  falling  drop,  tugs.  WP.D. 


ON  «  Oi    Surface  tension,  dynes.  % 

00  Ol    *J 


If 

O        M 


8  S 

ON 


I»MMMWMMNMM 

M     KJ     ON  Oi    ^4 


WF.D. 

7. 


Itl 


t 


«'-'" 


H-  H- 

0     O     K) 

M  M  M  M  M  .»' 

b  b  M 

^i  Oi    O 

jo  23  5  S  * 

^ 

II 

0?  ^ 

vO     ON 

1!           II 

rr*  n™ 
O/*^    k\ 

1 
^ 

\J       Is} 

M  -S  -b 

X—  S    Oi 

*•  o  *M  o  S  ep 

Oi  Oi  to  *^j  O  *^ 

Oi  Oi  ON  -^4  4»>  a) 

i6 

sion,  together  with  the  data  necessary  for  the  calculations.  The  surface 
tensions  given,  except  those  for  water,  are  interpolated  from  the  results — 
determined  under  the  same  conditions  as  our  drop  weights,  i.  e.,  against 
saturated  air — of  Renard  and  Guye,1  those  for  water  being  interpolated 
from  the  results  of  Ramsay  and  Shields,2  against  the  vapor  pressure  of  the 
liquid.  Kp  D  ,  KF  D  ,  and  Kc  D  ,  in  Table  I,  and  KF  D  in  Tables  II  and  III, 
are  the  factors  by  which  the  surface  tension  in  dynes  must  be  multiplied 
to  give  the  drop  weight,  in  milligrams,  from  these  tips.  KF  D  is  the  con- 
stant already  mentioned  in  the  real  analytical  expression  of  Tate's  laws,, 
when  the  same  tip  is  employed.  The  tips  used  in  Tables  I,  II,  and  III, 
although  made  from  the  same  tubing,  have  slightly  different  diameters 
exposed,  owing  to  the  bevels  being  cut  at  slightly  different  angles.  The 
diameter  of  the  tubing  itself  was  about  6.5  millimeters. 

Table  I  shows  the  reason  for  determining  the  weight  of  only  the  falling 
drop  with  the  more  delicate  form  of  apparatus. 

In  order  that  errors  in  the  interpolations  of  the  values  of  surface  ten- 
sion, as  well  as  possible  errors  in  the  surface  tensions  themselves,  might 
not  influence  the  conclusions  as  to  the  accuracy  of  Tate's  laws,  in  Table 
III,  where  the  determinations  are  the  most  accurate,  a  check,  has  been 
secured  without  any  direct  comparison  with  surface  tension,  by  substi- 
tuting the  drop  weights,  of  the  same  liquid  at  two  different  temperatures, 
for  the  surface  tensions  in  the  well-known  law  of  Ramsay  and  Shields, 
and  then  comparing  the  constancy,  for  the  various  liquids,  of  the  constant,, 
^temp.  with  that  of  those  of  Ramsay  and  Shields,  (&R  &  s )  and  Renard  and 
Guye  (kR  &  G).  In  other  words,  for  7-  in  dynes,  in  the  relation 


=£  =  2.12  ergs,* 


has  been  substituted  WFT>  in  milligrams,  so  that  if  surface  tension  (as 
altered  by  temperature)  and  falling  drop  weight  are  proportional,  for 
any  one  liquid  from  the  same  tip,  one  should  find  the  expression 


ft y  —  &temp. 

just  as  constant  as  the  other  for  all  so-called  "non-associated"  liquids. 

1  J.  chim.  phys.,  5,  81  (1907). 

2  Z.  physik.  Chem.,  12,  431  (1893). 

8  M  is  here  the  molecular  weight  as  a  liquid,  d  the  density,  and  t  the  temperature. 


All  the  densities  are  interpolated  from  results  found  in  the  literature  * 
as  were  also  those  of  both  Ramsay  and  Shields,  and  Renard  and  Guye, 
so  that  uniformity  in  the  compared  results  is  thus  secured. 

All  chemicals,  with  the  exception  of  guaiacol  (Table  I),  which  was  im- 
pure, were  specially  purified  for  the  purpose. 

The  drop  volumes  throughout  are  each  the  average  of  several  deter- 
minations, the  extreme  variation  in  tube  3  (Table  III)  being  0.2-0.4  per 
cent. 

TABLE  IV. 
Drop  weights  for  various  tip  diameters,     t  =  27°. 

WF.D. 
WF.D. 


6. 190 

8.764 


D. 
Substance.  DI  =  4.68  mm.  D2  =  6.22     D3=7.i2.  Da.  D2. 

Benzene 26.10         34-6o         39. 15         5-577         5-563 

Chlorbenzene 29 . 70        40 . 40        45 . 10        6 . 348         6 . 495 

Quinoline 41. 15         55.00        62.40         8.792         8.843 


In  Table  IV  are  given  the  drop  weights  issuing  from  beveled  tips  of 
various  diameters.  These  results  are  not  as  accurate  as  some  of  the  others, 
for  tube  2  was  used  as  the  burette,  and  the  error  in  measuring  the  lower 
end  of  the  bevel  is  necessarily  large.  Under  K'  are  the  values  of  tfre  con- 
stant of  Tate's  first  law,  i.  e.,  weight  of  falling  drop  divided  by  the  diame- 
ter of  the  tip. 

TABLE  V. 


Substance. 

Alcohol.   .  . 

>-v-  7 

Rounded  tip. 
Temp.    A  in  Fig.  3. 

58.4          0.907 
21.5          0.934 

•   /   lor  ups    01  various  lorms. 
Approx- 
Bevel  at  30°.               Sharpened  edge,  s^face 

Temp.     B  i 
60.  1 
22.5 
65.0 
22.1 

n  Fig.  3. 
.070 
.090 
.119 
.127 

Temp.    C  in  Fig.  3. 
21.  1           1.123 

tensions. 

19 
22 
21 
29 

Benzene.  .  .  . 

.... 

.  . 

Chlorbenzene 

64.0 

0.932 

67-9 

.109 

27 

22.5 

0.965 

24.0 

.129 

22.0           I.I45 

32 

Quinoline.  .  . 

64.0 

1.024 

72.0 

.164 

....               ... 

38 

Water 

21.0 
23.1 

I.04I 
I.OSO 

22.6 
25-5 

.189 
.220 

22.6             I.I57 
21.0             I.I55 

43 
72 

Average 0.983+0.025 

1  Approximately  of  same  diameter. 


i.i35±o.oi7 


.  I45±o.oo8 


18 

Table  V  gives  the  results  obtained  by  use  of  tips  of  various  forms,  but 
of  approximately  the  same  diameter  (see  Fig.  3).  Tip  A,  here,  is  rounded 
at  the  end,  B  has  a  bevel  at  an  angle  of  about  30°,  not  sufficient  to  have 


ABC 

Fig.  3- 

the  effect  of  a  sharp  edge,  and  C,  without  bevel,  has  a  very  sharp  edge. 
All  these  were  measured  in  tube  2,  and  consequently  the  determinations 
are  not  as  accurate  as  those  in  Table  III. 

TABLE  VI. — CRITICAL  TEMPERATURES.1 

Prom 
Fr°m  7(^)2/3  =  k(r-d). 


Substance.  M-\d/  R.  &  G.«  R.  &  S.«  Observed. 

Benzene 286.6  285.8-289.6  288  280.6-296.4 

Chlorbenzene 354-1  357.2-358.4  359-7  360.0-362.2 

Pyridine 352.0  344.7-346.9  342 

Aniline 439.4  448.1-449.1  404.9  425.7 

Quinoline 492 . 3  495 . 6-496 . 9  466 .  i  <52O 

And,  finally,  in  Table  VI,  are  the  critical  temperatures  of  the  liquids 
in  Table  III,  as  calculated  by  the  substitution  of  the  drop  weight,  Wp  D , 
and  kicmp  for  the  surface  tension  7-,  and  k  in  the  Ramsay  and  Shields  rela- 
tion, 

y(^)"/3=(r-6), 

where  r  is  the  difference  between  the  critical  temperature  and  that  of  ob- 
servation, and  M,  d  and  k  have  the  same  meaning  as  before. 

Discussion  of  Results. 

It  will  be  seen,  even  from  Table  I,  where  the  experimental  error  in  drop 
weight  is  comparatively  large,  that  Contrary  to  the  conclusion  of  Guye 

1  Here,  in  all  cases,  the  temperature  coefficient  (k  or  ktemp.)  used  is  the  one  found 
for  the  specific  liquid,  and  not  the  average  values. 

2  Calculated  extremes  from  surface  tensions. 
8  Given  by  Ramsay  and  Shields,  Loc.  cit. 


19 

and  Perrot,  the  relationship  between  drop  weight,  from  a  properly  con-1 
structed  tip,  and  surface  tension  in  saturated  air,4  is  very  much  more  than  a 
first  approximation,  even  when  the  liquids  examined  include  that  giving 
the  highest,  and  that  giving  almost  the  lowest,  surface  tension  known, 
i.  e.,  water  at  70.6  and  ether  at  16.8  dynes  per  centimeter. 

The  results  in  Table  II  make  this  conclusion  even  more  striking,  for 
they  show  that  much  of  the  variation  in  I  is  due  to  experimental  error. 
And,  finally,  Table  III,  where  the  accuracy  in  the  determination  of  drop 
volume  and  drop  weight  was  the  greatest  possible  at  the  time,  shows  the 
variation  in  the  constant  relationship,  for  some  of  the  same  liquids  ex- 
amined in  I  and  II,  to  be  very  small  indeed.  Here,  with  five  liquids,5 
varying  in  surface  tension  from  25.88  to  52.62  dynes,  each  being  studied 
at  two  temperatures,  the  mean  value  of  KF  D  for  all  cases,  from  a  certain 
tip,  is  1.226  ;+ 0.0026;  the  mean  error  of  a  single  result  being  +0.0083. 

Although  in  these  results  the  error  is  small,  the  discrepancy  is  still  too 
great — granting  the  accuracy  of  the  drop  weights  and  surface  tensions — to 
conclude  that  the  proportionality  is  rigidly  exact;  even  though  the  agree- 
ment is  about  as  good  as  that  observed  in  results  for  surface  tensions  by 
different  methods,  and  little  worse  than  that  shown  in  the  results  by  any 
one  method,  by  different  observers.  The  error  in  drop  weight  cannot 
in  any  case  exceed  0.4  per  cent.,  taking  all  things  into  consideration,  and 
is  generally  much  less,  consequently  the  discrepancy  is  only  to  be  explained 
either  by  errors  in  the  interpolated  surface  tensions,  or  by  actual  failure 
of  the  law  of  proportionality  to  hold  closer  than  this  (due  possibly  to  a  very 
slight  and  variable,  but  unnoticeable,  rise  of  the  liquids  on  the  walls  of 
the  tip).  When  it  is  remembered,  however,  that  the  interpolations  of  the 
values  for  surface  tension  were  made  from  smoothed  curves,  which  could 
not  always  be  made  to  pass  through  all  the  few  points  available,  it  becomes 
very  apparent  that  in  some  cases  errors  in  the  interpolated  surface  tensions 
even  as  high  as  one  per  cent.,  are  quite  possible.  If  this  be  true,  the  law 
of  the  proportionality  between  falling  drop  weight  (from  a  proper  tip) 
and  surface  tension  becomes  rigid.  To  prove  this  directly  and  conclusively 
has  been  impossible,  for  it  could  be  done  only  by  aid  of  a  more  delicate 

4  According  to  Renard  and  Guye,  surface  tensions  in  saturated  air  and  those  un- 
der the  vapor  pressure  of  the  liquid  do  not  differ  by  more  than  0.5  per  cent. 

6  Unfortunately,  ether  could  not  be  used  in  either  tube  2  or  tube  3,  owing  to  in- 
terference of  a  bulb;  and  the  volume  of  tube  3  was  too  small  to  permit  water  to  be 
used  with  the  beveled  tip. 


2O 

apparatus,  with  measurements  of  drop  weights  at  the  exact  temperatures 
at  which  the  surface  tensions  themselves  have  been  determined.1  Below, 
however,  it  is  shown  that  the  interpolated  values  of  surface  tension  for 
any  one  liquid  are  burdened  with  error,  so  that  analogy  would  force  the 
conclusion  that  they,  also,  are  at  the  root  of  the  error  when  different  liquids 
are  considered. 

The  conclusion  follows  then,  from  Tables  I,  II,  and  III,  and  from  the  be- 
havior of  tip  C  in  Table  V,  that  Tate's  second  law — the  weight  of  a  falling 
drop  (from  a  proper  tip)  is  proportional  to  the  surface  tension  (against 
saturated  air)  of  the  liquid — is  true.  Because  surface  tensions  calculated 
from  drop  weights  agree,  even  with  those  possibly  faultily  interpolated 
from  results  by  capillary  rise,  as  well  as  those  determined  by  other  meth- 
ods agree  with  these,  when  directly  determined. 

Consideration  of  the  columns  &temp  ,  £R  &  G.,  and  kK  &  s  ,  in  Table  III,  shows 
that  the  constants,  though  calculated  from  results  at  only  two  tempera- 
tures, are  as  constant  as  those  of  Renard  and  Guye,  which  are  in  each 
case  the  mean  of  determinations  made  at  several  pairs  of  temperatures, 
and  are  very  much  more  constant  than  those  of  Ramsay  and  Shields,2  from 
results  at  two  temperatures.  It  will  also  be  observed  that  the  variation 
of  &temp.  from  its  mean  value  is  always  (when  worth  considering)  in  the  same 
direction  as  that  of  Renard  and  Guye's,  for  the  same  liquid. 

This  certainly  proves  conclusively  that,  with  any  one  liquid,  from  any  one 
tip,  drop  weight  is  proportional  to  the  surface  tension,  as  it  is  altered  by  changes 
in  temperature,  for,  by  substitution  of  drop  weight  for  surface  tension  in  the 
Ramsay  and  Shields  expression,  leaving  out  any  direct  comparison  with 
the  interpolated  values  of  surface  tensions,  a  result  is  obtained  which  is  as 
•constant  as  that  found  by  the  use  of  directly  determined — not  interpolated — 
surface  tensions.  And  this  is  true  when  the  interpolated  values  of  surface 
tension  at  the  two  temperatures  lead  to  a  discrepancy  in  the  two  values  of 
KF  D  ,  as  calculated  for  that  liquid.  Although  this  proof  is  not  direct,  as  far 
as  concerns  different  liquids,  it  leaves  very  little  possibility  of  the  slight  dis- 
crepancy in  KF  D  being  due  to  anything  but  the  errors  in  the  interpolated  sur- 
face tensions  as  concluded  above. 

We  would  conclude  from  the  constancy  of  &temp.,  in  Table  III,  then: 

1  This  is  now  being  done  in  this  laboratory. 

2  Although  Ramsay  and  Shields' s  values  were  calculated  from  surface  tensions  ob- 
served under  different  conditions,  their  constants  are  still  to  be  compared  with  the 
others  as  to  constancy. 


21 

That  Tale's  third  law —  the  weight  of  a  falling  drop  decreases  with  in- 
creased temperature — is  true.  And,  further,  that  the  change  in  drop 
weight  for  a  change  in  temperature  can  be  calculated  accurately  for  non- 
associated  liquids,  by  the  substitution  of  the  drop  weight  at  one  tempera- 
ture for  the  surface  tension,  and  &temp  for  k  in  the  Ramsay  and  Shields 
relation 


-*, 


and  solving  for  the  other  drop  weight. 

Or,  knowing  the  drop  weights,  &temp.,  and  the  densities,  it  is  possible  to 
find  the  molecular  weight  of  the  liquid,  with  an  accuracy  equal  to  that 
attained  when  surface  tensions  are  employed  directly  in  the  above  rela- 
tion. 

Since  the  molecular  temperature  coefficient,  &temp>,  is  found  to  be  constant, 
it  is  possible,  by  extrapolation,  to  find  the  temperature  at  which  the  drop 
weight  would  become  zero;  i.  e.,  the  critical  temperature  of  the  liquid,  for  at 
that  point  the  drop  would  disappear,  there  being  then  no  distinction  be- 
tween the  gas  and  the  liquid.  It  is  only  necessary,  for  this  calcula- 
tion, to  substitute  WT  D  for  7-  and  &temp.  for  k,  in  the  other  form  of  the  Ram- 
say and  Shields  relation,  i.  e., 


and  solve  for  the  critical  temperature  (r  plus  the  temperature  at  which  7- 
(or  WF  D  )  is  determined).  (See  Table  VI.) 

It  must  be  remembered  here,  however,  that  in  all  cases  in  which  this 
method  has  been  applied,  it  has  been  done  so  at  a  disadvantage,  for  only  two 
points  were  had  through  which  to  draw  the  curve.  Further  than  that  I  have 
worked  at  low  temperatures  (never  above  80°),  and  consequently  must 
extrapolate  from  these  two  points  through  a  much  greater  distance  than 
either  Renard  and  Guye,  or  Ramsay  and  Shields,  from  their  larger  number. 
The  first  objection  holds  for  all  the  liquids,  though  least  for  benzene,  but 
the  second  hardly  affects  benzene,  for  73.2°  is  not  far  from  its  boiling-point. 
With  all  high-boiling  liquids,  both  objections  hold,  and  both  increase  with 
the  boiling  point  (and  critical  temperature). 

From  the  equal  constancy  of  ktemp  and  k,  however,  it  is  evident  that  just  as 
accurate  critical  temperatures  can  be  calculated  from  drop  weights  as  from 
surface  tensions,  against  saturated  air,  provided  in  both  cases  the  determinations, 


22 

from  which  the  molecular  temperature  coefficients  are  found,  are  made  at 
as  many  temperatures,  and  carried  to  as  high  a  temperature. 

Table  IV,  it  is  thought,  shows  that  from  such  tips,  between  these  diam- 
eters, there  is  a  direct  proportionality  between  drop  weight  and  diameter 
of  the  tip  (Tale's  first  law).  At  least  there  is  no  decided  trend  in  the  pro- 
portional factor,  for  it  varies  just  as  one  might  expect  it  to  from  the  known, 
and  fairly  large,  experimental  error.  It  must  be  remembered  that  tips 
larger  than  the  diameter  of  the  maximum  drop  would  always  deliver  one 
constant  maximum  drop  weight;  while,  when  the  tip  becomes  small,  there 
is  probably  a  point  beyond  which  the  drop  will  not  decrease  appreciably 
in  weight  for  a  considerable  change  in  diameter,  for  it  would  then  be 
difficult  to  prevent  in  any  way  the  rise  of  liquid  upon  walls  of  the  tip. 

Table  V  shows  that  when  rounded,  a  tip  behaves  differently  from  the  one 
in  Table  III ;  the  liquid  rises  to  various  heights  on  the  outer  walls,  and  the 
diameter  of  the  basis  for  the  drop  varies  with  the  nature  of  the  liquid. 
This  is  also  true,  though  to  a  lesser  degree,  with  the  tube  that  is  insuffi- 
ciently beveled.  In  neither  case  is  KFI)  even  approximately  constant. 
Tip  C,  on  the  other  hand,  compares  very  favorably  with  the  other  beveled 
one,  used  with  Tube  2  (Table  II).  Whatever  theory  may  be  advanced, 
then,  as  to  the  tip,  it  will  be  seen  that  the  point  to  be  considered  is  the 
effect  of  the  tip  (Tate's  "sharp  edge")  in  delimiting  the  portion  upon 
which  the  drop  can  hang,  especially  by  preventing  the  rise  of  liquid  upon 
the  walls,  for  that  would  be  variable  with  different  liquids,  and  lead  to 
variable  weights.  Undoubtedly  it  is  only  the  failure  to  follow  Tate's 
directions  in  this  respect  that  has  caused  the  determinations  of  drop 
weights,  since  his  time,  to  negative  his  conclusions. 

Summary. 

The  results  of  this  investigation  may  be  summarized  as  follows: 

1.  An  apparatus  is  described  by  which  it  is  possible  to  make  a  very  accu- 
rate estimation  of  the  volume  of  a  single  drop  of  liquid  falling  from  a  tube, 
and  consequently  of  its  weight. 

2.  With  this  apparatus  was  used  a  capillary  tip,  beveled  at  an  angle 
of  45°,  which,  contrary  to  those  used  by  other  investigators,  had  the  same 
effect  as  the  one  originally  used  by  Tate,  i.  e.,  it  delimits  the  area  of  the  tip 
wetted,  by  preventing  the  rise  of  liquid  upon  the  walls,  and  thus  forces 
all  liquids  to  drop  from  one  and  the  same  area. 


23 

3-  It  is  shown  that  whenever  this  effect  is  obtained,  either  by  use  of  a 
properly  beveled  tube,  or  one  ground  to  a  sharp  edge,  the  drop  weight 
has  a  different  meaning  than  it  has  when  the  drop  is  formed  on  either  a 
rounded  tip,  or  on  one  insufficiently  beveled. 

4.  The  falling  drop  from  a  capillary  tip,  and  not  the  pendant  drop,  is 
proportional  in  weight  to  that  of  the    falling   drop    from    a   thin-walled 
tube  with  a  sharp  edge. 

5.  From   such   tips   as   were   used,    it  is  concluded  that  Tate's  second 
law — the  weight  of  a  drop,  other  things  being  the  same,  is  proportional 
to  the  surface  tension  (against  saturated  air)  of  the  liquid — is  true. 

6.  It  is  shown  that  from  such  a  tip,  Tate's  third  law — the  weight  of  a 
•drop  is  decreased  by  an  increase  in  temperature — is  true. 

7.  Falling  drop  weights  for  the  same  liquid  at  two  temperatures,  from 
such  a  tip,  can  be  substituted  for  the  surface  tensions  in  the  relation  of 
Ramsay  and  Shields,  and  molecular  weights  in  the  liquid  state  calculated 
with  an  accuracy  equal  to  that  possible  by  aid  of  surface  tensions,  under 
the  same,  saturated  air,  conditions.     And,  by  aid  of  this  formula,  know- 
ing the  molecular  weight  of  a  non-associated  liquid,  the  falling  drop  weight 
at  one  temperature,  and  the  densities,  it  is  possible  to  calculate  the  weight 
of  the  drop  falling  from  the  same  tip  at  another  temperature. 

8.  Critical  temperatures  can  be  calculated  by  aid  of  Ramsay  and  Shields' s 

(M\  2f 
—  )     3  =  k(r — 6),  by  substituting  a  drop  weight  for  surface 

tension,  and  the  molecular  temperature  coefficient  of  drop  weight  for  k,  with 
the  same  accuracy  attained  by  the  use  of  surface  tensions  (against  saturated 
air),  provided  the  drop  weights  (from  which  the  coefficient  is  found)  are 
determined  at  as  many  temperatures,  and  at  as  high  a  temperature  as 
the  surface  tensions. 

9.  For  beveled  tips,  when  the  diameters  lie  between  4.68  and  7.12  mm., 
Tate's  first  law — the  drop  weight  of  any  one  liquid  is  proportional,  under 
like  conditions,  to  the  diameter  of  the  dropping  tube — is  true. 


BIBLIOGRAPHY  OF  DROP  WEIGHT— ALPHABETICALLY  ARRANGED. 


Autonow,  G.  N. 
Bolle,  J. 
Duclaux. 
Dupre". 

Eschbaum,  F. 
Guglielmo,  G. 
Guthrie. 
Guye  and  Perrot. 

Hagen. 

Hannay,  J.  B. 

Kohlrausch,  F. 

Lebaigue. 

Leduc  and  Larcdote. 

Lohnstein,  F. 

Mathieu. 

Ollivier. 

Rayleigh. 

Rosset. 

Tate,  T. 

Traube. 

Volkmann,  P. 
Worthington. 


J.  chim.  phys.,  5,  372  (1907). 

Geneva  Dissertation,  1902. 

Ann.  chim.  phys.,  4th  ser.,  21,  386  (1870). 

Ibid.,  9,  345  (1866). 

Ber.  pharm.  Ges.,  Heft  4,  1900. 

Accad.  Lincei  Atti.,  12,  462  (1904);  15,  287  (1906). 

Proc.  Roy.  Soc.,  13,  444  (1864). 

Arch,  scien.  phys.  et  naturelle,  4th  ser.,  n,  225  (1901);  4t 

ser.,  15,  312  (1903). 
Berl.  Akad.,  78,  1845. 
Proc.  Roy.  Soc.  Edin.,  437,  1905. 
Ann.  phys.,  20,  798  (1906);  22,  191  (1907). 
J.  pharm.  chim.,  7,  87  (1868). 
J.  phys.,  i,  364  and  716  (1902). 
C.  r.,  134,  589;  135,  95  and  732  (1902). 

Ann.  phys.,  20,  237  and  606;  21,  1030  (1906);  22,  737  (1907). 
J.  phys.  [2],  3,  203  (1884). 
Ann.  chim.  phys.,  8th  ser.,  10,  229  (1907). 
Phil.Mag.,  5th  ser.,  20,  321  (1899). 
Bull.  soc.  chim.,  23,  245  (1900). 
Phil.  Mag.,  27,  176  (1864). 
J.  pr.  Chem.  [2],  34,  292  and  515  (1886). 
Ber.,  19,  874  (1886). 
Ann.  physik.  (2),  n,  206. 
Proc.  Roy.  Soc.,  32,  362  (1881). 
Phil.  Mag.,  5th  ser.,   18,   461    (1884);  19,   46   (1885);  20,   $ 

(1885). 


BIOGRAPHY. 


Reston  Stevenson  was  born  May  5,  1882,  in  Wilmington,  N.  C.  He 
received  the  degree  of  A.B.  at  the  University  of  North  Carolina,  June, 
1902 ;  A.M.  at  the  same  institution,  June,  1903.  During  the  years  1 903-^4 
and  1 904-' 05  he  was  assistant  instructor  in  chemistry  at  The  Cornell 
University  where  he  pursued,  simultaneously,  graduate  work  in  chemistry 
and  physics.  In  May,  1905,  he  accepted  a  position  as  research  chemist 
with  the  Eastern  Dynamite  Company.  He  left  this  company  to  become 
chemist  at  the  Hudson  River  Works  of  the  General  Chemical  Company. 
In  September,  1906,  he  left  the  General  Chemical  Company  to  become 
Tutor  in  Chemistry  at  the  College  of  the  City  of  New  York,  and  still 
occupies  this  position.  He  has  at  the  same  time  completed  his  graduate 
work  for  the  degree  of  Ph.D.  at  Columbia  University. 


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